Systems and methods for characterizing a central axis of a bone from a 3D anatomical image

ABSTRACT

Presented herein are efficient and reliable systems and methods for calculating and extracting three-dimensional central axes of bones of animal subjects—for example, animal subjects scanned by in vivo or ex vivo microCT platforms—to capture both the general and localized tangential directions of the bone, along with its shape, form, curvature, and orientation. With bone detection and segmentation algorithms, the skeletal bones of animal subjects scanned by CT or microCT scanners can be detected, segmented, and visualized. Three dimensional central axes determined using these methods provide important information about the skeletal bones.

RELATED APPLICATIONS

This application claims priority to U.S. application Ser. No. 16/155,943filed Oct. 10, 2018 which claims priority of U.S. application Ser. No.15/081,788 (U.S. Pat. No. 10,136,869 issued Nov. 27, 2018) filed Mar.25, 2016, the entire disclosure of which is hereby incorporated hereinby reference.

TECHNICAL FIELD

This invention relates generally to methods and systems of imageanalysis. More particularly, in certain embodiments, the inventionrelates to detection and localization of a bone central axis from animage of a subject (e.g., mammal), e.g., captured with a computedtomography (CT) scanner.

BACKGROUND

There is a wide array of technologies directed to in vivo and ex vivoimaging of mammals—for example, bioluminescence, fluorescence, X-raycomputed tomography, and multimodal imaging technologies. In vivoimaging of small mammals and ex vivo imaging of samples from smallmammals is performed by a large community of investigators in variousfields, e.g., oncology, infectious disease, and drug discovery.

Micro computed tomography (hereafter, “microCT”) imaging, is anx-ray-based technology that can image tissues, organs, and non-organicstructures with an extremely high resolution. MicroCT has evolvedquickly, requiring low dose scanning and fast imaging protocols tofacilitate multi-modal applications and enable longitudinal experimentalmodels. Similarly, nano-computed tomography (nanoCT) systems designedfor high-resolution imaging of ex vivo samples are also now used.Multi-modal imaging involves the fusion of images obtained in differentways, for example, by combining fluorescence molecular tomography (FMT),PET, MRI, CT, and/or SPECT imaging data.

Conventional image analysis applications and/or imaging systemstypically allow for visualization, analysis, processing, segmentation,registration and measurement of biomedical images. These applicationsand systems also provide volume rendering tools (e.g., volumetriccompositing, depth shading, gradient shading, maximum intensityprojection, summed voxel projection, signal projection); manipulationfunctions (e.g., to define areas of structures of interest, deleteunwanted objects, edit images and object maps); and measurementfunctions (e.g., calculation of number of surface voxels, number ofexposed faces, planar area of a region, estimated surface area of aregion).

Acquisition of animal images can be time consuming, and rapid analysisof the acquired images is key to the efficiency of the process. Threedimensional (3D) imaging software, including microCT image analysis,enables extraction of structural, biological, and anatomical attributesfrom images, such as thickness, porosity, anisotropy, and othermeasures, of organs of interest, such as bones. Due to the anatomicalcontrast and high spatial resolution provided by microCT systems, theyare widely used for studying skeletal bone formation, structure, anddiseases. Automation of such analyses improves throughput, accuracy, andefficacy. In classical bone analysis approaches, researchers wererequired to visually and manually quantify the structural attributes ofbones using printed images produced by the microCT platform. While someimage analysis systems have been developed for computer-aided boneanalysis, the digital workflows offered by bone analysis software stillrequire considerable manual input and interaction from users andresearchers. For example, such manual feedback is currently required toobtain stereological measures of cortical and trabecular bonecompartments, e.g., manual selection of discrete 2-D slices of a 3-Dbone image from which averaged thicknesses or other properties aredetermined.

Some conventional image analysis systems focus on locating the principalaxes of the bones to extract the direction of 2-D slices of the bone.But principal axes do not carry detailed shape and directionalinformation. Principal axes represent the major and minor directionalaxes of a bone, as shown in FIG. 1, and are defined as the eigenvectorsof the moment of inertia tensor of the bone volume. As shown in FIG. 1,principal axes do not capture detailed information regarding the shape,form, localized tangential directions, and curvature of the bone—all ofwhich impact the precision of automated stereological studies ofosteological structure and disease assessment. The principal axesprimarily indicate the general direction of a bone as a solid objectwithout fully capturing its shape and curvature. Moreover, the principalaxes are not useful in characterizing partially circular bones, e.g.,the pelvic girdle. As such, they are not useful for automating 2-Dslice-by-slice measurements and analysis.

There is a need for automated, precise, and improved methods forstereological analysis and slice-by-slice characterization of bones inimages, such as microCT images.

SUMMARY OF THE INVENTION

Automated detection of central axes of skeletal bones significantlyimproves the speed, efficiency, and automation of slice-by-slicemeasurements and analyses of bones. Central axes of long bones (e.g.,bones of the extremities that have a length greater than the width,e.g., femur) can effectively encapsulate the spatial features,direction, orientation, and shape of long bones. Calculation of centralaxes is essential for performing automated and accurate 2-Dslice-by-slice planar studies such as stereological studies on bones,for example, the femur and the tibia. The 2-D planes perpendicular tothe central axes constitute the slices that are used in 2-D boneanalysis or stereology measurements. Automated detection of bone centralaxis and the 2-D stereology slices allows for fully automatedcomputer-based stereological measurements of bones.

Presented herein are efficient and reliable systems and methods forcalculating and extracting three-dimensional central axes of skeletalbones of animal subjects—for example, animal subjects scanned by in vivomicroCT platforms and ex vivo samples of animal subjects scanned bymicroCT or nanoCT platforms—to capture both the general and localizedtangential directions of the bone, along with its shape, form,curvature, and orientation. With bone detection and segmentationalgorithms, the bones of animal subjects scanned by CT, nanoCT, ormicroCT scanners can be detected, segmented, and visualizedautomatically. Three dimensional central axes determined using thesemethods provide important information about the bones.

The detection and localization of central axes improves the speed andaccuracy of stereology studies performed visually and manually andcircumvents the limitations of principal axes and provides, inter alia,directional, shape, and curvature information regarding the bone. Thedetection and localization of central axes reveals a variety of featuresrelating to the shape, direction, and curvature of the bone that are notavailable through the existing method of using the principal axes. Thisis particularly useful for analysis of curved or non-straight longbones, and for 2-D slice-by-slice analysis, e.g., 2-D planarslice-by-slice stereology studies of the tibia or pelvic girdle. Thecentral axis of a bone represents the medial path that describes themain center-line, shape, and orientation of a bone.

An automated procedure for identifying a central bone axis is not asimple problem, since the procedure would need to accurately identifythe central bone axis for a wide range of sizes and shapes of the bonesbeing imaged (e.g., it would need to account for different kinds ofbones as well as variability between the same bone across multiplesubjects) without user interaction or training, and it would need to bea computationally efficient procedure.

Presented herein, in certain embodiments, are systems and methods forautomated computation of a bone central axis from a 3D anatomical image.An area of the subject (e.g., mammal) including a bone of interest isscanned (e.g., with a microCT system), and a 3D anatomical image of thearea of the subject is obtained. In some embodiments, in a first step, abinary mask of the bone of interest is filled using morphologicalprocessing. In some embodiments, the binary mask of the bone is filledby morphological processing to more accurately reflect the internalcomposition of the bone (e.g., to accurately model the distincttrabecular and cortical components of the bone). In some embodiments, ina second step, skeletonization (e.g., morphological skeletonization) isperformed on the filled bone by iterative 3-D thinning. In someembodiments, in a third step, the skeleton is pruned (e.g., thinned) andreduced to a single (e.g., a main and/or central) branch. In someembodiments, the skeleton is pruned down to the single branch andsmoothed, yielding a single-branched curve that follows the medial pathof the bone, effectively identifying and isolating the central axis ofthe bone.

Also described herein are systems and methods to efficiently fill themorphological holes on the six exterior faces of a three-dimensional(hereafter, “3-D”) binary image. Some embodiments described hereinrelate to systems and methods for filling 2-D morphological holes whichextend across three faces. In some embodiments, these morphologicalholes on the boundary are due to hollow internal compartments ofpartially out-of-view bones.

Some example embodiments described herein relate to calculating andextracting central axes of skeletal bones (e.g., long bones) to captureboth the general and localized tangential directions of the bones. Thecalculation of central axes also identifies, among other things, theshape, form, and curvature of the bones. That is, the central axisrepresents a medial path that describes, among other things, the maincenter-line, shape, and orientation of a long bone.

In one aspect, the invention is directed to a method for automaticallyidentifying a three-dimensional (3-D) central axis of a bone of interestin a 3-D image, the method comprising: receiving, by a processor of acomputing device, the 3-D image of one or more bones, comprising thebone of interest (i.e., at least a portion of the bone of interest), ofa mammal; isolating, by the processor, the bone of interest from the oneor more bones in the 3-D image (e.g., yielding an isolated image of anexterior surface of a cortical tissue of the bone of interest);generating, by the processor (e.g., after the isolating of the bone ofinterest), a binary bone mask of the bone of interest; generating, bythe processor, a filled bone mask for the bone of interest using thebinary bone mask; generating, by the processor, a skeleton of the boneof interest (e.g., by performing iterative 3-D thinning of the filledbone mask); and generating, by the processor, a pruned skeleton toreduce the skeleton to a branch (e.g., a single branch, central branch,and/or main branch) corresponding to the 3-D central axis of the bone ofinterest.

In certain embodiments, the bone of interest is a long bone of themammal (e.g., a femur, tibia, fibula, humerus, radius, ulna, metacarpal,metatarsal, phalange, and clavicle). In certain embodiments, the bone ofinterest is a non-long bone (e.g., a short bone, flat bone, sesamoidbone, or irregular bone) of the mammal (e.g., pelvic girdle).

In certain embodiments, the 3-D image is obtained by a computedtomography scanner (e.g., a micro computed or nano computed tomographyscanner). In certain embodiments, the 3-D image is captured in vivo. Incertain embodiments, the 3-D image is captured ex vivo. In certainembodiments, the 3-D image is a computed tomography image of an exteriorsurface of cortical tissue of the one or more bones.

In certain embodiments, generating the filled bone mask for the bone ofinterest comprises performing, by the processor, morphologicalprocessing of the portion of the 3-D image corresponding to the bone ofinterest, said processing comprising: performing 3-D binary dilation ofthe binary bone mask of the bone of interest (e.g., with a sphericalstructuring element) to form a dilated bone mask; and identifying andfilling borders and/or morphological holes (e.g., gaps and/ordiscontinuities) of the dilated bone mask, then processing the result(e.g., performing 3-D binary erosion on the result of the border andhole filling operations) to generate the filled bone mask for the boneof interest.

In certain embodiments, the method comprises filling borders of the boneof interest by: representing image data from the binary bone mask of thebone of interest digitally as one or more data-cubes; identifying avertex of a data-cube, the vertex having all edges connected to thevertex associated with true (e.g., binary true) voxels; forming a 2-Dimage from the three faces connected to the identified vertex (e.g., byadding an all-zero face as one of the quadrants and diagonallyconnecting binary true voxels on the boundaries of the all-zero facequadrant); filling morphological holes in the thusly formed 2-D image toproduce a filled surface; and mapping the filled surface back to thethree corresponding faces of the data-cube.

In certain embodiments, generating the 3-D skeleton of the bone ofinterest comprises performing, by the processor, morphologicalprocessing of the filled bone mask, the processing comprising performingiterative 3-D thinning of the filled bone mask.

In certain embodiments, generating the pruned 3-D skeleton comprisesperforming, by the processor, morphological processing of the skeletonfor the bone of interest, said processing comprising: identifying asingle-branched centerline tree or a single-cycle main loop of theskeleton as a main path; pruning the skeleton by removing minor branchesnot included in the main path; and smoothing the pruned skeleton (e.g.,by point averaging), thereby generating the pruned 3-D skeleton.

In certain embodiments, the method comprises characterizing the bone ofinterest according to the 3-D central axis corresponding to the bone ofinterest (e.g., identifying an abnormality of the bone and/oridentifying the bone as a specific bone of the mammal).

In certain embodiments, the method comprises rendering an image using atleast the 3-D central axis of the bone of interest.

In certain embodiments, the method comprises performing, by theprocessor, a stereological measurement of the bone of interest using theidentified 3-D central axis of the bone of interest, said performing ofthe stereological measurement comprising: producing a plurality ofgraphical 2-D cross-sections (e.g., 2-D image slices) of the bone ofinterest in planes perpendicular to the identified 3-D central axis atvarious locations along a length of the bone of interest; for each ofthe graphical 2-D cross-sections, determine a measurement of the bone asdepicted in the graphical 2-D cross section (e.g., identifying acortical thickness for each of the 2-D image slices); and obtaining thestereological measurement of the bone of interest using the measurementsdetermined from the plurality of graphical 2-D cross-sections (e.g.,obtaining an average cortical thickness for the bone of interest as anaverage of the measurements determined from the 2-D image slices).

In certain embodiments, the method comprises determining, by theprocessor, one or more of (i) to (iii)—(i) the presence of a diseasestate, (ii) a disease state risk, and/or (iii) an extent of diseaseprogression (e.g., staging of a disease)—using the identified 3-Dcentral axis of the bone of interest (e.g., based on one or morestereological measurements of the bone of interest determined using theidentified 3-D central axis of the bone of interest).

In another aspect, the invention is directed to a method ofautomatically filling borders in an image of an object (e.g., a bone) ofinterest, the method comprising: digitally representing image data froma binary mask of an object (e.g., a bone of interest) as one or moredata-cubes; identifying, by a processor of a computing device, a vertexof a data-cube of the one or more data-cubes, the vertex having alledges connected to the vertex associated with true (e.g., binary true)voxels; forming, by the processor, a 2-D image from the three facesconnected to the identified vertex (e.g., by adding an all-zero face asone of the quadrants and diagonally connecting binary true voxels on theboundaries of the all-zero face quadrant); filling, by the processor,morphological holes in the thusly formed 2-D image to produce a filledsurface; and mapping, by the processor, the filled surface back to thethree corresponding faces of the data-cube.

In another aspect, the invention is directed to a system forautomatically identifying a three-dimensional (3-D) central axis of abone of interest in a 3-D image, the system comprising: a processor; anda memory having instructions stored thereon, wherein the instructions,when executed by the processor, cause the processor to: receive the 3-Dimage of one or more bones, comprising the bone of interest (i.e., atleast a portion of the bone of interest), of a mammal; isolate the boneof interest from the one or more bones in the 3-D image (e.g., yieldingan isolated image of an exterior surface of a cortical tissue of thebone of interest); generate (e.g., after the isolating of the bone ofinterest), a binary bone mask of the bone of interest; generate a filledbone mask for the bone of interest using the binary bone mask; generatea skeleton of the bone of interest (e.g., by performing iterative 3-Dthinning of the filled bone mask); and generate a pruned skeleton toreduce the skeleton to a branch (e.g., a single branch, central branch,and/or main branch) corresponding to the 3-D central axis of the bone ofinterest.

In certain embodiments, the bone of interest is a long bone of themammal (e.g., a femur, tibia, fibula, humerus, radius, ulna, metacarpal,metatarsal, phalange, and clavicle). In certain embodiments, the bone ofinterest is a non-long bone (e.g., a short bone, flat bone, sesamoidbone, or irregular bone) of the mammal (e.g., pelvic girdle). In certainembodiments, the 3-D image is obtained by a computed tomography scanner(e.g., a micro computed or nano computed tomography scanner).

In certain embodiments, the 3-D image is captured in vivo. In certainembodiments, the 3-D image is captured ex vivo. In certain embodiments,the 3-D image is a computed tomography image of an exterior surface ofcortical tissue of the one or more bones.

In certain embodiments, the instructions cause the processor to generatethe filled bone mask for the bone of interest by performingmorphological processing of the portion of the 3-D image correspondingto the bone of interest, said processing comprising: performing 3-Dbinary dilation of the binary bone mask of the bone of interest (e.g.,with a spherical structuring element) to form a dilated bone mask; andidentifying and filling borders and/or morphological holes (e.g., gapsand/or discontinuities) of the dilated bone mask, then processing theresult (e.g., performing 3-D binary erosion on the result of the borderand hole filling operations) to generate the filled bone mask for thebone of interest.

In certain embodiments, the instructions cause the processor to fillborders of the bone of interest by: representing image data from thebinary bone mask of the bone of interest digitally as one or moredata-cubes; identifying a vertex of a data-cube, the vertex having alledges connected to the vertex associated with true (e.g., binary true)voxels; forming a 2-D image from the three faces connected to theidentified vertex (e.g., by adding an all-zero face as one of thequadrants and diagonally connecting binary true voxels on the boundariesof the all-zero face quadrant); filling morphological holes in thethusly formed 2-D image to produce a filled surface; and mapping thefilled surface back to the three corresponding faces of the data-cube.

In certain embodiments, the instructions cause the processor to generatethe 3-D skeleton of the bone of interest by performing morphologicalprocessing of the filled bone mask, the processing comprising performingiterative 3-D thinning of the filled bone mask.

In certain embodiments, the instructions cause the processor to generatethe pruned 3-D skeleton by performing morphological processing of theskeleton for the bone of interest, said processing comprising:identifying a single-branched centerline tree or a single-cycle mainloop of the skeleton as a main path; pruning the skeleton by removingminor branches not included in the main path; and smoothing the prunedskeleton (e.g., by point averaging), thereby generating the pruned 3-Dskeleton.

In certain embodiments, the instructions cause the processor tocharacterize the bone of interest according to a central axiscorresponding to the bone of interest (e.g., identifying an abnormalityof the bone and/or identifying the bone as a specific bone of themammal). In certain embodiments, the instructions cause the processor torender an image using at least the 3-D central axis of the bone ofinterest. In certain embodiments, the instructions cause the processorto perform a stereological measurement of the bone of interest using theidentified 3-D central axis of the bone of interest, said performing ofthe stereological measurement comprising: producing a plurality ofgraphical 2-D cross-sections (e.g., 2-D image slices) of the bone ofinterest in planes perpendicular to the identified 3-D central axis atvarious locations along a length of the bone of interest; for each ofthe graphical 2-D cross-sections, determining a measurement of the boneas depicted in the graphical 2-D cross section (e.g., identifying acortical thickness for each of the 2-D image slices); and obtaining thestereological measurement of the bone of interest using the measurementsdetermined from the plurality of graphical 2-D cross-sections (e.g.,obtaining an average cortical thickness for the bone of interest as anaverage of the measurements determined from the 2-D image slices). Incertain embodiments, the instructions cause the processor to determineone or more of (i) to (iii)-(i) the presence of a disease state, (ii) adisease state risk, and/or (iii) an extent of disease progression (e.g.,staging of a disease)—using the identified 3-D central axis of the boneof interest (e.g., based on one or more stereological measurements ofthe bone of interest determined using the identified 3-D central axis ofthe bone of interest).

In another aspect, the invention is directed to a system forautomatically filling borders in an image of an object (e.g., a bone) ofinterest, the system comprising: a processor; and a memory havinginstructions stored thereon, wherein the instructions, when executed bythe processor, cause the processor to: digitally represent image datafrom a binary mask of an object (e.g., a bone of interest) as one ormore data-cubes; identify a vertex of a data-cube of the one or moredata-cubes, the vertex having all edges connected to the vertexassociated with true (e.g., binary true) voxels; form a 2-D image fromthe three faces connected to the identified vertex (e.g., by adding anall-zero face as one of the quadrants and diagonally connecting binarytrue voxels on the boundaries of the all-zero face quadrant); fillmorphological holes in the thusly formed 2-D image to produce a filledsurface; and map the filled surface back to the three correspondingfaces of the data-cube.

Embodiments described with respect to one aspect of the invention maybe, applied to another aspect of the invention (e.g., features ofembodiments described with respect to one independent claim arecontemplated to be applicable to other embodiments of other independentclaims).

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects, features, and advantages ofthe invention will become more apparent and may be better understood byreferring to the following description taken in conjunction with theaccompanying drawings, in which:

FIG. 1 is an image illustrating the principal axes of the tibia of amouse imaged by a microCT scanner;

FIG. 2 is an image illustrating an automated 3D skeletonization of anelliptical prism annexed by conical sections on top and bottom;

FIG. 3 is an image showing a 3-D representation of the bones of the hindlimb of a mouse imaged by a microCT scanner segmented using splittingfilters, according to an illustrative embodiment of the presentdisclosure;

FIG. 4 is a flow chart showing a method of automated characterizationand calculation of a central bone axis, according to an illustrativeembodiment of the present disclosure;

FIG. 5 is an image illustrating a central axis of a tibia of a mouseimaged by a microCT scanner, according to an illustrative embodiment ofthe present disclosure;

FIG. 6 is a flow chart showing a morphological bone filling method,according to an illustrative embodiment of the present disclosure;

FIGS. 7A-7E are example images created following steps of themorphological bone filling method of FIG. 6, according to anillustrative embodiment of the present disclosure;

FIG. 8 is a flow chart showing a border filling method on a 3D binarybone image (data-cube), according to an illustrative embodiment of thepresent disclosure;

FIGS. 9A-9F are example images created following steps of the borderfilling method of FIG. 8, according to an illustrative embodiment of thepresent disclosure;

FIG. 10 is an image illustrating a skeleton of the tibia of a mouseimaged by microCT scanner; the image was computed using iterative 3-Dthinning on the filled bone, according to an illustrative embodiment ofthe present disclosure;

FIG. 11 is a flow chart showing a method for pruning and smoothing ofthe morphological skeleton of a bone, according to an illustrativeembodiment of the present disclosure;

FIG. 12A-12H are images created following steps of the pruning andsmoothing method of FIG. 11 applied to 3D image of a mouse tibia,according to an illustrative embodiment of the present disclosure;

FIG. 13A-13D are example images illustrating results of 2-Dslice-by-slice stereology operations performed automatically on a 3Dimage of a mouse tibia following central axis determination, accordingto an illustrative embodiment of the present disclosure.

FIG. 14 is a block diagram of an example computing device and an examplemobile computing device, for use in illustrative embodiments of thepresent disclosure;

FIG. 15 is a block diagram of an example computing environment, for usein illustrative embodiments of the present disclosure.

DETAILED DESCRIPTION

It is contemplated that systems, devices, methods, and processes of theclaimed invention encompass variations and adaptations developed usinginformation from the embodiments described herein. Adaptation and/ormodification of the systems, devices, methods, and processes describedherein may be performed by those of ordinary skill in the relevant art.

Throughout the description, where articles, devices, and systems aredescribed as having, including, or comprising specific components, orwhere processes and methods are described as having, including, orcomprising specific steps, it is contemplated that, additionally, thereare articles, devices, and systems of the present invention that consistessentially of, or consist of, the recited components, and that thereare processes and methods according to the present invention thatconsist essentially of, or consist of, the recited processing steps.

It should be understood that the order of steps or order for performingcertain action is immaterial so long as the invention remains operable.Moreover, two or more steps or actions may be conducted simultaneously.

The mention herein of any publication, for example, in the Backgroundsection, is not an admission that the publication serves as prior artwith respect to any of the claims presented herein. The Backgroundsection is presented for purposes of clarity and is not meant as adescription of prior art with respect to any claim.

As used herein, an “image”—for example, a 3-D image of mammal—includesany visual representation, such as a photo, a video frame, streamingvideo, as well as any electronic, digital or mathematical analogue of aphoto, video frame, or streaming video. Any apparatus described herein,in certain embodiments, includes a display for displaying an image orany other result produced by the processor. Any method described herein,in certain embodiments, includes a step of displaying an image or anyother result produced via the method.

As used herein, “extracting” or “extraction” of bone axes refers to thedetection, segmentation, calculation, visualization, and the like, ofaxes (e.g., central axes) of bones.

As used herein, “3-D” or “three-dimensional” with reference to an“image” means conveying information about three dimensions. A 3-D imagemay be rendered as a dataset in three dimensions and/or may be displayedas a set of two-dimensional representations, or as a three-dimensionalrepresentation.

As used herein, “long bone” means a bone of an extremity (e.g., of amammal, e.g., mouse, rat, etc.) that has a length greater than the width(e.g., femur bone). In some embodiments, a long bone is a bone of thelegs, the arms, the hands, the feet, the fingers, the toes, or collarbones. In some embodiments, a long bone is selected from the following:femora, tibiae, fibulae, humeri, radii, ulnae, metacarpals, metatarsals,phalanges, and clavicles (e.g., of collar bones). Certain embodimentsdescribed herein apply to either long bones or non-long bones,including, for example, short bones, flat bones, sesamoid bones, andirregular bones. In certain embodiments, non-long bones include boneswith partially circular shapes, e.g., the pelvic girdle.

As used herein, a “mask” is a graphical pattern that identifies a 2-D or3-D region and is used to control the elimination or retention ofportions of an image or other graphical pattern.

Described herein are systems and methods for automated detection of bonecentral axes from in vivo or ex vivo images (e.g., 3-D images). In someexample embodiments, the 3-D image is an in vivo image of an animalsubject (e.g., a mammal such as a mouse). In some embodiments, the 3-Dimage is an ex vivo image of a sample (e.g., bone sample) from an animalsubject (e.g., a mammal such as a mouse). In some embodiments, imagescan be acquired and/or processed by medical imaging devices such as CTscanners, microCT scanners, and the like. It should be understood thatan image, such as a 3-D image, may be a single image or a set or seriesof multiple images.

Central axes of bones can effectively encapsulate characteristics anddata of bones, including, for example, spatial features, direction,orientation, and shape of a bone. Using bone detection and segmentationalgorithms, the skeletal bones of animal subjects (e.g., scanned by CTor microCT scanners) are detected, segmented, and visualized, as shownin FIG. 3. When visualizing a collection of bones, the bone axeseffectively represent the orientation of the bones relative to eachother. The bone axes are also useful for determining bone directions(e.g., during computer-based analysis), as the axes carry quantitativestructural information such as the spatial angle of the boneorientation. Importantly, the 2-D planes perpendicular to the centralaxes are used for slice-by-slice stereology analysis of bones. By movingalong the central axis and extracting 2-D planes normal to the centralaxis, 2-D slice-by-slice analyses such as stereology can be carried outas shown in FIG. 13 A-D, described in more detail below.

Some example embodiments described herein relate to calculating andextracting central axes of skeletal bones to capture both the generaland localized tangential directions of the bones. The calculation ofcentral axes also identifies, among other things, the shape, form, andcurvature of the bones. That is, the central axis represents a medialpath that describes, among other things, the main center-line, shape,and orientation of a bone.

Description and calculation of bone central axes is challenging becausebones are not homogeneous solid objects with simple regular shapes; theycan take arbitrary shapes and include hollow regions and holes withvarious densities and porosities. In addition, morphological skeletonsof binary bone masks, which reduce 3D regions into line sets, may not berepresented by a single-branched axis, but rather, they may includemultiple branches, especially at the distal ends, confoundingtraditional analysis. Thus, in certain embodiments, mere 3Dskeletonization of a binary bone mask, or even a filled bone mask, isfound to be insufficient for extracting a central axis. As shown in FIG.2, skeletonization of solid objects results in multi-branched trees orgraphs which cannot serve as a medial or central axis. Peripheralbranches of skeletons only reflect certain regional spatial attributesof the solid object. 3D skeletonization reduces a solid object into aset of curved lines, only some of which carry information useful forcalculation of the solid object's central axis; thus, in certainembodiments, further steps, as described herein, may be performed toextract the central axis of a solid object from its morphologicalskeleton in an accurate, automated, and reproducible way.

In certain embodiments, bone central axes are extracted frommorphological skeletons. Skeletons are generally defined for filled 2-Dor 3-D binary objects. In some embodiments, a skeleton may berepresented and/or illustrated as a skeletal tree. In some embodiments,in filled 3-D objects, the morphological skeleton is extracted byperforming iterative thinning on the 3-D object binary mask. The processof extracting the morphological skeleton is referred to asskeletonization. In some embodiments, skeletonization involvesextracting the locus of the center of all maximally inscribed spheres ina 3-D object. Referring to FIG. 2, the result of direct skeletonizationof an elliptical prism annexed by conical sections is displayed. For 3-Dobjects elongated in a certain direction, the skeleton is oftencomprised of a main branch that extends through the object, and a fewminor branches that extend from the main branch to the boundary of theobject, similar to the skeleton shown in FIG. 2.

Results of direct 3-D skeletonization of bones are often not usefulcandidates for the central axis calculation and extraction due to twoprimary reasons. First, a skeletal bone is almost never a homogenouslyfilled 3-D object, and its inner compartment (e.g., the trabeculae), isa porous structure distributed over the marrow. A direct 3-Dskeletonization of the bone mask (without undergoing filling operations)would represent the medial tree spanning the cortical shell andtrabecular network of the bone, rather than the morphological skeletonof the bone in its entirety including the cortical, trabecular, andmarrow compartments. Second, because of peripheral branches (e.g.,multi-branched segments extending into the conical sections 210, 212),the skeleton, in its raw form, is not a single-branched central axisthat represents the orientation and form of a 3-D object. The peripheralbranches of the 3-D skeleton only carry localized structural informationespecially at the distal ends and are not useful in guiding andautomating slice-by-slice measurements.

FIG. 3 shows a 3-D image comprising multiple bones of a mammal,according to an exemplary embodiment. More specifically, FIG. 3illustrates bones of the hind limb of a mouse (e.g., imaged by a microCTscanner) that are segmented into a femur, tibia, and patella, usingsplitting filters.

In FIG. 3, the bones 302, 304, 306, 308 have been morphologicallyisolated and/or segmented from one another. Other bones have also beenisolated, including the individual vertebrae 310. Various commonapproaches may be taken toward isolating and/or segmenting theindividual bones of the 3-D image, as shown in FIG. 3, for example, thesystems and methods described in U.S. patent application Ser. No.14/812,483, filed Jul. 29, 2015, entitled, “Systems and Methods forAutomated Segmentation of Individual Skeletal Bones in 3D AnatomicalImages,” the text of which is incorporated herein by reference in itsentirety. In certain embodiments, isolation and/or segmentation employslinear classification or regression, and a signal to noise ratio (S/N)corresponding to one or more features may be used to measure quality ofclassification or regression. In certain embodiments, constraints forclassification or regression are chosen empirically. For example, insome embodiments, constraints for classification or regression arechosen by running the same set of examples several times with varyingconstraints. Appropriate constraints may be chosen to strike a balancebetween accuracy and computing time in the isolation and/or segmentationalgorithm chosen.

FIG. 4 illustrates a flow chart for extracting a central bone axis froman isolated binary bone mask, according to an exemplary embodiment.Prior to identifying (e.g., extracting) the central axis of the bone, a3-D image (or a series of 3-D images) of the bones of a mammal isreceived, for example, from a CT or micro-CT scanner [402]. The bone(from which the axis is to be calculated) is morphologically isolatedand/or segmented from a collection of bones [404], so that only the boneof interest (e.g., long bone) is analyzed. Morphological isolationand/or segmentation is described above in further detail with referenceto FIG. 3.

After morphological isolation, the 3-D image of the bone(s) is convertedto a binary bone mask [406]. In several embodiments, a 3-D binary bonemask is a three-dimensional array comprising voxels in an included(e.g., binary true) or excluded (e.g., binary false) state. A voxel inthe binary true state in the mask corresponds to a region containingbone tissue in the 3-D image of the bone(s). Conversely, a voxel in abinary false state in the mask corresponds to an empty or non-bonetissue in the 3-D image. As such, in certain embodiments, the binarybone mask represents at least the cortical and trabecular compartmentsof the bone(s). In further embodiments, the binary bone mask isinitially filled (e.g., the interior portion contents such as marrow) bybinary true voxels (e.g., the binary bone mask represents a solid 3Dbone volume composed of cortical, trabecular, and marrow compartments).An example technique for generating a binary bone mask is furtherdescribed in detail in U.S. patent application Ser. No. 14/162,693 filedJan. 23, 2014, which is incorporated herein by reference in itsentirety.

In certain embodiments, the binary mask of the bone is filled bymorphological processing [408], which is described in further detail inthe flowchart depicted in FIG. 6. In certain embodiments, filling a 3-Dobject (e.g., a binary bone mask) generally refers to the process ofidentifying the internal voxels (e.g., the internal sub-volume boundedby the surface) of the object and adding all of them to the binary bonemask (e.g., by changing their states to binary true). In someembodiments, skeletonization is performed on the filled bone byiterative 3-D thinning [410], which is described in detail below. Insome embodiments, the skeleton is pruned (e.g., minor branches areremoved) down to a single branch (e.g., the trunk) and smoothed [412],an illustrative method for which is described in detail in the flowchartdepicted in FIG. 11. In certain embodiments, these three steps (408,410, and 412) yield a single-branched curve that follows the medial pathof the bone, effectively identifying and isolating the central axis ofthe bone.

Referring to FIG. 5, the result of the central bone axis identificationmethod described in reference to FIG. 4 is shown. The central bone axis502 is obtained after the steps outlined in FIG. 4 are carried out,including pruning and smoothing the 3D morphological skeleton of thefilled binary bone mask.

FIG. 6 is a flowchart of a process for filling a binary mask of a bone(e.g., bone filling) using morphological processing, according to anexemplary embodiment. Bone filling is a step in extracting the centralaxis of a bone, e.g., step 408 of the method depicted in FIG. 4. Forexample, in certain embodiments, bone filling is performed by adding theinternal compartment (e.g., marrow) of the bone to the bone mask. Thepresence of cracks or veins in the bone shell that connect the internalpart or marrow of the bone to the background of the bone mask make bonefilling more challenging. Because of the veins and/or cracks in the boneshell, the internal compartment is morphologically connected to thebackground, and additional steps are required for accurate, robustdetection of the internal compartment of the bone. For example, in someembodiments, the internal compartment is detected by performing a binarysubtraction (e.g., an AND NOT operation) between dilated masks of thebone before and after morphological filling. In certain embodiments,dilation refers to expansion of an image, proportionately ordisproportionately, along any axis or direction. In some embodiments,the dilation is 3-D spherical dilation performed using a sphericalstructuring element of a size ranging from 3-5. Various methods ofdilation may be employed. Further discussion of dilation and relatedoperations are discussed in International Application PCT/IB2011/002757,filed Sep. 12, 2011, published as International Patent ApplicationPublication No. WO/2013/038225, which is incorporated herein byreference in its entirety. In some embodiments, the internal compartmentof the bone is obtained by dilating the result of this subtraction. Insome embodiments, border filling in the bone filling process isperformed by applying 2-D filling to the border planes of the data-cubecontaining the bone image stack, as outlined in detail in the flowchartof FIG. 8.

Still with reference to FIG. 6, a binary bone mask is generated [602](e.g., retrieved) from a medical image such as a CT or a microCT scan ofone or more bones of a mammal. In certain embodiments, the various bonescontained in the image are automatically isolated and/or segmented (seeFIG. 3). For illustrative purposes, the binary bone mask generated instep 602 is herein referred to as Image0, although the method does notrely on any particular name being assigned to any image. In turn, thebinary bone mask (Image0) is dilated, by a spherical structuringelement, e.g., of size 3-10 depending on the metric voxel dimensions ofthe image, and the dilated binary bone mask is stored as Image1 [604].

The borders of Image1 are then identified and filled [606].Morphological holes (e.g., gaps and/or discontinuities) are also filled[608]. Border filling is described in more detail below with referenceto FIG. 8. Then, 3D binary erosion is performed [610] to produce thefilled bone mask [622].

In certain embodiments, the result of the 3D hole filling and borderfilling operations is stored as Image2. Image1 is then subtracted fromImage2 [610], resulting in a mask effectively representing the locationof filled holes and cracks. In certain embodiments, small spots, definedas connected components with volumes smaller than empirically determinedbounds, are removed from the resulting mask and the image is againdilated, and stored as Image3. In turn, a new image is generated bycombining Image0 with Image3, resulting in the binary bone mask ofImage0 superimposed with the filled holes represented by Image3. Theborders of the resulting image (Image0+Image3) are filled andsubsequently the holes of the 3D image are filled. The holes areidentified as the empty or binary false voxels located in the internalcompartment of the dilated bone mask (morphologically disconnected fromthe background image by the dilated bone mask). The holes are filled bybeing added to the bone mask (or their voxel values being updated to 1or binary true).

FIGS. 7A-7E show the results of the steps described in reference to FIG.6. FIG. 7A depicts two views—external and cut-away—of the result of thebinary bone mask, step 602 of the method of FIG. 6. FIG. 7B depicts theresult of 3D binary dilation, step 604 of the method of FIG. 6. FIG. 7Cdepicts the result of border filling operations, step 606 of the methodof FIG. 6. FIG. 7D depicts the result of morphological hole filling,step 608 of the method of FIG. 6. FIG. 7E depicts the filled bone maskresulting from 3D binary erosion, step 610 of the method of FIG. 6.

FIG. 8 illustrates a process for performing border filling, according toan exemplary embodiment. In some example embodiments, border filling isperformed during the process of generating a binary bone mask (e.g.,FIG. 6). Border filling is performed on an unprocessed or processed bonemask (e.g., a dilated bone image resulting from step 604 of FIG. 6).

More specifically, to initiate border filling, the binary bone mask usedin the exemplary embodiment of FIG. 6 is retrieved [602]. In someembodiments, image data (e.g., of the binary bone mask) is representeddigitally as one or more data-cubes. In various embodiments, a data-cubecomprises a 3D array of values corresponding to voxels in the 3-D bonemask including twelve edges and eight vertices, each of the verticesbeing associated with three edges. Each edge of the data-cube isassociated with two faces. A first data-cube vertex is selected from theeight vertices [804], an example of which is shown in FIG. 9A. Theselected vertex is checked to ensure all three edges connected to thevertex contain voxels belonging to the binary mask [806]. If an edgeconnected to a vertex contains a binary mask voxel, it is associatedwith and/or assigned a true (e.g., binary true) state. If all of theedges connected to the selected vertex are associated with true voxels,the vertex check is satisfied. Otherwise, if the vertex check does notpass, the next vertex is selected. If the vertex passes the voxel check,a 2-D image is formed by concatenating the three faces connected to thevertex with an all-zero face as a quadrant [808], an example of which isshown in FIG. 9B. Pixels with binary true values bordering the all-zeroquadrant are then connected diagonally by updating the values of thecorresponding pixels of the all-zero quadrant to binary true [810], asdepicted in FIG. 9C. Morphological holes in the resulting concatenated2-D image are then filled and the filled surfaces are mapped back to thethree corresponding faces of the data-cube [812], as depicted in FIG. 9D(2-D image) and FIGS. 9E and 9F (two views of the resulting data-cube).

If all of the vertices have been checked and processed (e.g., completed)[816], the method proceeds to step 818. Otherwise, the method returns toselect the next vertex in the data-cube, in step 804. With all verticescompleted, a first data-cube edge is selected [818]. The edge is checkedto ensure both of the faces connected to the edge and the edge itselfcontain binary true voxels [820]. If the edge check is passed (e.g.,edge is associated with true voxels), a 2-D image is formed fromconcatenating the two faces connected to edge [822]. Otherwise the nextdata-cube edge is selected as in step 818. Morphological holes in the2-D image are filled and the filled surfaces are mapped back to the twocorresponding faces of the data cube [824]. If all edges have beencompleted [826], the method continues to step 828, otherwise the nextedge is selected. After all edges are completed, the holes on eachindividual face of the data-cube are filled [830], thereby generating aborder-filled bone mask. The border-filled bone mask is stored in memory[828].

As mentioned above, identifying a central bone axis also includes a stepof 3-D thinning. The concept of 3-D thinning is described in more detailin Building Skeleton Models via 3-D medial Surface/Axis ThinningAlgorithms (Lee, T. C., Graphical Models and Image Processing, Vol. 56,No. 6, November, pp. 462-478, 1994), which is incorporated herein byreference in its entirety.

Generally, 3-D thinning shrinks or reduces solid objects, areas, orvolumes, such as a filled 3-D object (e.g., bone) to a morphologicalskeleton (see FIG. 10), with major and minor branches. In someembodiments, the skeleton (or the medial surface) of a structure is thelocus of the center of all maximally inscribed spheres of the object in3-D space (e.g., Euclidean space) where each of the spheres touch theboundary at more than one point. In some embodiments, a distancetransformation is used to thin the 3-D image. In some embodiments,border points are repetitively deleted under topological and geometricalconstraints until a smaller set of connected points is acquired. In someembodiments, the 3-D skeleton substantially represents or is anapproximation of the “true” skeleton in the 3-D Euclidean space. In someembodiments, level set marching approaches are performed.

More specifically, the iterative deletion of border points provides 3-Dthinning while maintaining topological properties of the image beingthinned. In some embodiments, each thinning iteration is divided intosubcycles according to the type of border point (e.g., north, south,west, east, up, bottom). The border points that are deleted arerestricted based on topological and geometric constraints, for example,to avoid undesired object separation or elimination in the image. Insome implementations, medial surface thinning (MST) and/or medial axisthinning (MAT) may be used as geometric constraints of the borderdeletion process of a 3-D thinning operation. That is, MST is used toidentify surface points that are not deleted during thinning. That is,medial surface thinning identifies surfaces that are approximatelylocated to a center line. MAT differs from MST in that the extractedskeleton consists of arcs and/or curves instead of surfaces thatapproximate the center line. MST and MAT are both described in furtherdetail in Building Skeleton Models via 3-D medial Surface/Axis ThinningAlgorithms (Lee, T. C., Graphical Models and Image Processing, Vol. 56,No. 6, November, pp. 462-478, 1994), which is incorporated herein byreference in its entirety.

FIG. 10 shows a 3-D skeletonization of a filled bone mask from the tibiaof a mouse, according to an exemplary embodiment. The skeleton 902 maybe further pruned and smoothed, as shown below with reference to FIG.11.

FIG. 11 illustrates a process [1100] of pruning and smoothing a skeletonto yield the central axis of the bone, according to an exemplaryembodiment. First a binary skeleton mask is retrieved [1102].Subsequently, a particular path (e.g., a main or central path) in theskeleton is identified [1104], e.g., by finding (i) the centerline treeof the skeleton (for example, via the method described in “TEASAR:tree-structure extraction algorithm for accurate and robust skeletonsSato, M.; Bitter, I.; Bender, M. A.; Kaufman, A. E.; Nakajima, M.Computer Graphics and Applications, 2000. Proceedings. The EighthPacific Conference on Volume, Issue, 2000 Page(s):281-449”) or (ii) asingle-cycle main loop of the skeleton, depending on whether the bonemorphological skeleton has a tree structure with no loops (e.g., longbones such as femur) which is often the case for mammalian bones, or thebone morphological skeleton has loops (e.g., pelvic girdle). In certainembodiments, the centerline tree of the skeleton is found using theTEASAR algorithm referenced above, which includes (1) reading binarysegmented voxels inside the object; (2) cropping the volume to just theobject; (3) computing the distance from boundary field (DBF); (4)computing the distance from any voxel field (DAF); (5) computing thepenalized distance from root voxel field (PDRF); (6) finding thefarthest PDRF voxel labeled as inside; (7) extracting the shortest pathfrom that voxel to the root; (8) labeling all the voxels near the pathas ‘used to be inside’; and (9) repeating steps 6 to 8 until no insidevoxels remain.

In the pruning step [1106], the minor branches of the skeleton areremoved from the identified main path, thus reducing the skeleton to asingle branch. To prevent the irregular shapes of the distal ends ofbones from affecting the central axis determination, the pruned branchis further smoothed by point averaging [1108]. The end result of thisstep is the bone central axis [1110], an example of which is illustratedin FIG. 5 at reference [502].

FIG. 12A-12H are images created following steps of the pruning andsmoothing method of FIG. 11, as applied to the tibia (FIGS. 12A-12D) andfemur (FIGS. 12E-12H) of a mouse scanned by a microCT imaging platformafter bone segmentation as shown in FIG. 3. From left to right, theimages show the bone mask (FIGS. 12A/12E), the result of theskeletonization step [1104] (FIGS. 12B/12F), the result of the pruningstep [1106] (FIGS. 12C/12G), and the result of the smoothing step [1108](FIGS. 12D/12H), thereby producing the central axis for the tibia andfemur.

In some implementations, the identified central axis of the bone is usedto quantify structural characteristics (e.g., features) of the bone,such as the bone's shape, form, localized tangential directions,curvature, and the like. These characteristics may be used, in turn, tocharacterize the bone, for example, by identifying abnormalities,identifying the bone as a specific bone, and the like. In someimplementations, the identified central axis is used to render images ofthe bone or the set of bones with which the bone is associated. Itshould be understood that the characteristics of a bone, identifiedusing the bone's central axis, can be used, for example, for otherimaging (e.g., rendering), diagnostics, and therapeutic purposes, aswell as for other applications.

For example, in certain embodiments, the identified central axis of thebone is used for stereological measurements and slice-by-slice studiesof the bone. FIG. 13A-13D are example images illustrating results of 2-Dslice-by-slice stereology operations performed accurately andautomatically following central axis determination. The planesperpendicular to the central axis are used to create 2-D image slices ofthe bone cross-section. Parameters such as average cortical thicknesscan then be calculated from these 2-D slices automatically. For example,FIG. 13A shows a mouse tibia 1300 following determination of the bonecentral axis per methods described herein. Planes 1302, 1306, and 1310are identified. These planes are perpendicular to the central axis atvarious locations along the length of the bone. Images of 2-Dcross-sections at these planes are obtained, e.g., images of FIGS.13B-13D. FIG. 13B corresponds to plane 1302, FIG. 13C corresponds toplane 1306, and FIG. 13D corresponds to plane 1310. From the 2-Dcross-sections, various bone properties can be determined, for example,average cortical (shell) thickness. Any number of cross-sections may betaken. In the case shown in FIG. 13, the average cortical thickness wasautomatically determined to be 3.98 voxels or 198 microns. The methoddisclosed herein provides an automated, robust way of obtaining thisinformation directly from a scan (e.g., micro-CT scan), therebyeliminating operator error and variability due to “by hand”measurements.

As discussed above, certain embodiments of the procedures describedherein relate to extracting the central axis of a bone to guidestereological measurements or capture, for example, of the direction,overall shape, and spatial characteristics of the bone. Various otherembodiments utilize the image processing methods described herein,including procedures such as border filling, bone filling, andpruning/smoothing, for other applications. For example, the imageprocessing methods described herein may be used in bonesegmentation/separation using morphological separation approaches suchas watershed. In some embodiments, the morphological separation isperformed on filled bones rather than the original bone masks. Moreover,border and bone filling are also useful in segmenting the cortical andtrabecular compartment of a bone, for example.

FIG. 14 shows an illustrative network environment 1400 for use in themethods and systems described herein. In brief overview, referring nowto FIG. 14, a block diagram of an exemplary cloud computing environment1400 is shown and described. The cloud computing environment 1400 mayinclude one or more resource providers 1402 a, 1402 b, 1402 c(collectively, 1402). Each resource provider 1402 may include computingresources. In some implementations, computing resources may include anyhardware and/or software used to process data. For example, computingresources may include hardware and/or software capable of executingalgorithms, computer programs, and/or computer applications. In someimplementations, exemplary computing resources may include applicationservers and/or databases with storage and retrieval capabilities. Eachresource provider 1402 may be connected to any other resource provider1402 in the cloud computing environment 1400. In some implementations,the resource providers 1402 may be connected over a computer network1408. Each resource provider 1402 may be connected to one or morecomputing device 1404 a, 1404 b, 1404 c (collectively, 1404), over thecomputer network 1408.

The cloud computing environment 1400 may include a resource manager1406. The resource manager 1406 may be connected to the resourceproviders 1402 and the computing devices 1404 over the computer network1408. In some implementations, the resource manager 1406 may facilitatethe provision of computing resources by one or more resource providers1402 to one or more computing devices 1404. The resource manager 1406may receive a request for a computing resource from a particularcomputing device 1404. The resource manager 1406 may identify one ormore resource providers 1402 capable of providing the computing resourcerequested by the computing device 1404. The resource manager 1406 mayselect a resource provider 1402 to provide the computing resource. Theresource manager 1406 may facilitate a connection between the resourceprovider 1402 and a particular computing device 1404. In someimplementations, the resource manager 1406 may establish a connectionbetween a particular resource provider 1402 and a particular computingdevice 1404. In some implementations, the resource manager 1406 mayredirect a particular computing device 1404 to a particular resourceprovider 1402 with the requested computing resource.

FIG. 15 shows an example of a computing device 1500 and a mobilecomputing device 1550 that can be used in the methods and systemsdescribed in this disclosure. The computing device 1500 is intended torepresent various forms of digital computers, such as laptops, desktops,workstations, personal digital assistants, servers, blade servers,mainframes, and other appropriate computers. The mobile computing device1550 is intended to represent various forms of mobile devices, such aspersonal digital assistants, cellular telephones, smart-phones, andother similar computing devices. The components shown here, theirconnections and relationships, and their functions, are meant to beexamples only, and are not meant to be limiting.

The computing device 1500 includes a processor 1502, a memory 1504, astorage device 1506, a high-speed interface 1508 connecting to thememory 1504 and multiple high-speed expansion ports 1510, and alow-speed interface 1512 connecting to a low-speed expansion port 1514and the storage device 1506. Each of the processor 1502, the memory1504, the storage device 1506, the high-speed interface 1508, thehigh-speed expansion ports 1510, and the low-speed interface 1512, areinterconnected using various busses, and may be mounted on a commonmotherboard or in other manners as appropriate. The processor 1502 canprocess instructions for execution within the computing device 1500,including instructions stored in the memory 1504 or on the storagedevice 1506 to display graphical information for a GUI on an externalinput/output device, such as a display 1516 coupled to the high-speedinterface 1508. In other implementations, multiple processors and/ormultiple buses may be used, as appropriate, along with multiple memoriesand types of memory. Also, multiple computing devices may be connected,with each device providing portions of the necessary operations (e.g.,as a server bank, a group of blade servers, or a multi-processorsystem).

The memory 1504 stores information within the computing device 1500. Insome implementations, the memory 1504 is a volatile memory unit orunits. In some implementations, the memory 1504 is a non-volatile memoryunit or units. The memory 1504 may also be another form ofcomputer-readable medium, such as a magnetic or optical disk.

The storage device 1506 is capable of providing mass storage for thecomputing device 1500. In some implementations, the storage device 1506may be or contain a computer-readable medium, such as a floppy diskdevice, a hard disk device, an optical disk device, or a tape device, aflash memory or other similar solid state memory device, or an array ofdevices, including devices in a storage area network or otherconfigurations. Instructions can be stored in an information carrier.The instructions, when executed by one or more processing devices (forexample, processor 1502), perform one or more methods, such as thosedescribed above. The instructions can also be stored by one or morestorage devices such as computer- or machine-readable mediums (forexample, the memory 1504, the storage device 1506, or memory on theprocessor 1502).

The high-speed interface 1508 manages bandwidth-intensive operations forthe computing device 1500, while the low-speed interface 1512 manageslower bandwidth-intensive operations. Such allocation of functions is anexample only. In some implementations, the high-speed interface 1508 iscoupled to the memory 1504, the display 1516 (e.g., through a graphicsprocessor or accelerator), and to the high-speed expansion ports 1510,which may accept various expansion cards (not shown). In theimplementation, the low-speed interface 1512 is coupled to the storagedevice 1506 and the low-speed expansion port 1514. The low-speedexpansion port 1514, which may include various communication ports(e.g., USB, Bluetooth®, Ethernet, wireless Ethernet) may be coupled toone or more input/output devices, such as a keyboard, a pointing device,a scanner, or a networking device such as a switch or router, e.g.,through a network adapter.

The computing device 1500 may be implemented in a number of differentforms, as shown in the figure. For example, it may be implemented as astandard server 1520, or multiple times in a group of such servers. Inaddition, it may be implemented in a personal computer such as a laptopcomputer 1522. It may also be implemented as part of a rack serversystem 1524. Alternatively, components from the computing device 1500may be combined with other components in a mobile device (not shown),such as a mobile computing device 1550. Each of such devices may containone or more of the computing device 1500 and the mobile computing device1550, and an entire system may be made up of multiple computing devicescommunicating with each other.

The mobile computing device 1550 includes a processor 1552, a memory1564, an input/output device such as a display 1554, a communicationinterface 1566, and a transceiver 1568, among other components. Themobile computing device 1550 may also be provided with a storage device,such as a micro-drive or other device, to provide additional storage.Each of the processor 1552, the memory 1564, the display 1554, thecommunication interface 1566, and the transceiver 1568, areinterconnected using various buses, and several of the components may bemounted on a common motherboard or in other manners as appropriate.

The processor 1552 can execute instructions within the mobile computingdevice 1550, including instructions stored in the memory 1564. Theprocessor 1552 may be implemented as a chipset of chips that includeseparate and multiple analog and digital processors. The processor 1552may provide, for example, for coordination of the other components ofthe mobile computing device 1550, such as control of user interfaces,applications run by the mobile computing device 1550, and wirelesscommunication by the mobile computing device 1550.

The processor 1552 may communicate with a user through a controlinterface 1558 and a display interface 1556 coupled to the display 1554.The display 1554 may be, for example, a TFT (Thin-Film-Transistor LiquidCrystal Display) display or an OLED (Organic Light Emitting Diode)display, or other appropriate display technology. The display interface1556 may comprise appropriate circuitry for driving the display 1554 topresent graphical and other information to a user. The control interface1558 may receive commands from a user and convert them for submission tothe processor 1552. In addition, an external interface 1562 may providecommunication with the processor 1552, so as to enable near areacommunication of the mobile computing device 1550 with other devices.The external interface 1562 may provide, for example, for wiredcommunication in some implementations, or for wireless communication inother implementations, and multiple interfaces may also be used.

The memory 1564 stores information within the mobile computing device1550. The memory 1564 can be implemented as one or more of acomputer-readable medium or media, a volatile memory unit or units, or anon-volatile memory unit or units. An expansion memory 1574 may also beprovided and connected to the mobile computing device 1550 through anexpansion interface 1572, which may include, for example, a SIMM (SingleIn Line Memory Module) card interface. The expansion memory 1574 mayprovide extra storage space for the mobile computing device 1550, or mayalso store applications or other information for the mobile computingdevice 1550. Specifically, the expansion memory 1574 may includeinstructions to carry out or supplement the processes described above,and may include secure information also. Thus, for example, theexpansion memory 1574 may be provided as a security module for themobile computing device 1550, and may be programmed with instructionsthat permit secure use of the mobile computing device 1550. In addition,secure applications may be provided via the SIMM cards, along withadditional information, such as placing identifying information on theSIMM card in a non-hackable manner.

The memory may include, for example, flash memory and/or NVRAM memory(non-volatile random access memory), as discussed below. In someimplementations, instructions are stored in an information carrier and,when executed by one or more processing devices (for example, processor1552), perform one or more methods, such as those described above. Theinstructions can also be stored by one or more storage devices, such asone or more computer- or machine-readable mediums (for example, thememory 1564, the expansion memory 1574, or memory on the processor1552). In some implementations, the instructions can be received in apropagated signal, for example, over the transceiver 1568 or theexternal interface 1562.

The mobile computing device 1550 may communicate wirelessly through thecommunication interface 1566, which may include digital signalprocessing circuitry where necessary. The communication interface 1566may provide for communications under various modes or protocols, such asGSM voice calls (Global System for Mobile communications), SMS (ShortMessage Service), EMS (Enhanced Messaging Service), or MMS messaging(Multimedia Messaging Service), CDMA (code division multiple access),TDMA (time division multiple access), PDC (Personal Digital Cellular),WCDMA (Wideband Code Division Multiple Access), CDMA2000, or GPRS(General Packet Radio Service), among others. Such communication mayoccur, for example, through the transceiver 1568 using aradio-frequency. In addition, short-range communication may occur, suchas using a Bluetooth®, Wi-Fi™, or other such transceiver (not shown). Inaddition, a GPS (Global Positioning System) receiver module 1570 mayprovide additional navigation- and location-related wireless data to themobile computing device 1550, which may be used as appropriate byapplications running on the mobile computing device 1550.

The mobile computing device 1550 may also communicate audibly using anaudio codec 1560, which may receive spoken information from a user andconvert it to usable digital information. The audio codec 1560 maylikewise generate audible sound for a user, such as through a speaker,e.g., in a handset of the mobile computing device 1550. Such sound mayinclude sound from voice telephone calls, may include recorded sound(e.g., voice messages, music files, etc.) and may also include soundgenerated by applications operating on the mobile computing device 1550.

The mobile computing device 1550 may be implemented in a number ofdifferent forms, as shown in the figure. For example, it may beimplemented as a cellular telephone 1580. It may also be implemented aspart of a smart-phone 1582, personal digital assistant, or other similarmobile device.

Various implementations of the systems and techniques described here canbe realized in digital electronic circuitry, integrated circuitry,specially designed ASICs (application specific integrated circuits),computer hardware, firmware, software, and/or combinations thereof.These various implementations can include implementation in one or morecomputer programs that are executable and/or interpretable on aprogrammable system including at least one programmable processor, whichmay be special or general purpose, coupled to receive data andinstructions from, and to transmit data and instructions to, a storagesystem, at least one input device, and at least one output device.

These computer programs (also known as programs, software, softwareapplications or code) include machine instructions for a programmableprocessor, and can be implemented in a high-level procedural and/orobject-oriented programming language, and/or in assembly/machinelanguage. As used herein, the terms machine-readable medium andcomputer-readable medium refer to any computer program product,apparatus and/or device (e.g., magnetic discs, optical disks, memory,Programmable Logic Devices (PLDs)) used to provide machine instructionsand/or data to a programmable processor, including a machine-readablemedium that receives machine instructions as a machine-readable signal.The term machine-readable signal refers to any signal used to providemachine instructions and/or data to a programmable processor.

To provide for interaction with a user, the systems and techniquesdescribed here can be implemented on a computer having a display device(e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor)for displaying information to the user and a keyboard and a pointingdevice (e.g., a mouse or a trackball) by which the user can provideinput to the computer. Other kinds of devices can be used to provide forinteraction with a user as well; for example, feedback provided to theuser can be any form of sensory feedback (e.g., visual feedback,auditory feedback, or tactile feedback); and input from the user can bereceived in any form, including acoustic, speech, or tactile input.

The systems and techniques described here can be implemented in acomputing system that includes a back end component (e.g., as a dataserver), or that includes a middleware component (e.g., an applicationserver), or that includes a front end component (e.g., a client computerhaving a graphical user interface or a Web browser through which a usercan interact with an implementation of the systems and techniquesdescribed here), or any combination of such back end, middleware, orfront end components. The components of the system can be interconnectedby any form or medium of digital data communication (e.g., acommunication network). Examples of communication networks include alocal area network (LAN), a wide area network (WAN), and the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

While the invention has been particularly shown and described withreference to specific preferred embodiments, it should be understood bythose skilled in the art that various changes in form and detail may bemade therein without departing from the spirit and scope of theinvention as defined by the appended claims.

What is claimed is:
 1. A method comprising: receiving, by a processor ofa computing device, a 3-D image of a 3-D object representing a bone ofinterest of a mammal; identifying, by the processor, internal voxelscorresponding to an internal sub-volume of the bone of interest;generating, by the processor and based on the identified internalvoxels, a filled bone mask of the bone of interest; generating, by theprocessor, a skeleton of the filled bone mask, wherein the skeletoncomprises a plurality of branches through the 3-D object; determining,by the processor and based on the plurality of branches, a 3-D centralaxis of the bone of interest, wherein the 3-D central axis correspondsto a medial path through the 3-D object; and generating an imageindicating at least the 3-D central axis of the bone of interest.
 2. Themethod of claim 1, further comprising: generating, by the processor, abinary bone mask of the bone of interest; and wherein the generating thefilled bone mask for the bone of interest is further based on the binarybone mask.
 3. The method of claim 1, wherein the 3-D image is obtainedby a computed tomography scanner.
 4. The method of claim 1, wherein thesurface of the bone of interest is an exterior surface of corticaltissue of the bone of interest.
 5. The method of claim 1, whereingenerating the filled bone mask for the bone of interest furthercomprises performing, by the processor, morphological processing of the3-D object representing the bone of interest, said morphologicalprocessing comprising: generating, by the processor, a binary bone maskof the bone of interest; and performing 3-D binary dilation of thebinary bone mask of the bone of interest to form a dilated bone mask;and identifying and filling borders, internal voxels, and/ormorphological holes of the dilated bone mask, and then processing theresult to generate the filled bone mask for the bone of interest.
 6. Themethod of claim 5, wherein the morphological processing furthercomprises: performing 3-D binary dilation of the binary bone mask of thebone of interest to form a dilated bone mask; and wherein theidentifying and filling borders, internal voxels, and/or morphologicalholes of the bone mask further comprises identifying and fillingborders, internal voxels, and/or morphological holes of the dilated bonemask.
 7. The method of claim 5, wherein filling borders of the bone ofinterest further comprises: representing image data from the binary bonemask of the bone of interest digitally as one or more data-cubes;identifying a vertex of a data-cube, the vertex having all edgesconnected to the vertex associated with true voxels; forming a 2-D imagefrom three faces connected to the identified vertex of the data-cube;filling morphological holes in the formed 2-D image to produce a filledsurface; and mapping the filled surface back to the three facesconnected to the identified vertex of the data-cube.
 8. The method ofclaim 1, wherein generating the skeleton of the bone of interestcomprises performing, by the processor, morphological processing of thefilled bone mask.
 9. The method of claim 1, wherein the determining the3-D central axis of the bone of interest further comprises: generating,by the processor, a thinned skeleton of the bone of interest.
 10. Themethod of claim 9, wherein generating the thinned skeleton furthercomprises: identifying a single-branched centerline tree or asingle-cycle main loop of the skeleton as a main path; removing minorbranches not included in the main path; and smoothing the resultingskeleton with the removed minor branches, thereby generating the thinnedskeleton.
 11. The method of claim 1, further comprising: characterizingthe bone of interest according to the 3-D central axis corresponding tothe bone of interest.
 12. The method of claim 1, wherein the internalsub-volume of the bone of interest comprises an internal solidsub-volume of the bone of interest.
 13. The method of claim 1, furthercomprising: performing, by the processor, a stereological measurement ofthe bone of interest using the determined 3-D central axis of the boneof interest, said performing of the stereological measurementcomprising: producing a plurality of graphical 2-D cross-sections of thebone of interest in planes perpendicular to the determined 3-D centralaxis at various locations along a length of the bone of interest; foreach of the graphical 2-D cross-sections, determining a measurement ofthe bone as depicted in the graphical 2-D cross section; and obtainingthe stereological measurement of the bone of interest using themeasurements determined from the plurality of graphical 2-Dcross-sections.
 14. The method of claim 1, further comprising:determining, by the processor and using the determined 3-D central axisof the bone of interest, one or more of: (i) a presence of a diseasestate, (ii) a disease state risk, or (iii) an extent of diseaseprogression.
 15. A system comprising: a processor; and a memory havinginstructions stored thereon, wherein the instructions, when executed bythe processor, cause the processor to: receive, by a processor of acomputing device, a 3-D image of a 3-D object representing a bone ofinterest of a mammal; identify, by the processor, internal voxelscorresponding to an internal sub-volume of the bone of interest;generate, by the processor and based on the identified internal voxels,a filled bone mask of the bone of interest; generate, by the processor,a skeleton of the filled bone mask; and determine, by the processor andbased on the skeleton, a 3-D central axis of the bone of interest,wherein the 3-D central axis corresponds to a medial path through the3-D object.
 16. The system of claim 15, generating, by the processor, abinary bone mask of the bone of interest; and generating, by theprocessor, the filled bone mask for the bone of interest using thebinary bone mask.
 17. The system of claim 15, wherein generating thefilled bone mask for the bone of interest further comprises: performing,by the processor, morphological processing of the 3-D objectrepresenting the bone of interest, said morphological processingcomprising: generating, by the processor, a binary bone mask of the boneof interest; and performing 3-D binary dilation of the binary bone maskof the bone of interest to form a dilated bone mask; and identifying andfilling borders, internal voxels, and/or morphological holes of thedilated bone mask, and then processing the result to generate the filledbone mask for the bone of interest.
 18. The system of claim 17, whereinfilling borders of the bone of interest further comprises: representingimage data from the binary bone mask of the bone of interest digitallyas one or more data-cubes; identifying a vertex of a data-cube, thevertex having all edges connected to the vertex associated with truevoxels; forming a 2-D image from three faces connected to the identifiedvertex of the data-cube; filling morphological holes in the formed 2-Dimage to produce a filled surface; and mapping the filled surface backto the three faces connected to the identified vertex of the data-cube.19. The system of claim 15, wherein the determining the 3-D central axisof the bone of interest further comprises: generating a thinned skeletonof the bone of interest.
 20. A non-transitory computer readable storagemedia comprising computer readable instructions that, when executed by aprocessor, cause a computing device to receive a 3-D image of a 3-Dobject representing a bone of interest of a mammal; identify, by theprocessor, internal voxels corresponding to an internal sub-volume ofthe bone of interest; generate, based on the identified internal voxels,a filled bone mask of the bone of interest; generate a skeleton of thebone of interest by performing 3D thinning; and determine, based on theskeleton, a 3-D central axis of the bone of interest, wherein the 3-Dcentral axis corresponds to a medial path through the 3-D object. 21.The non-transitory computer readable storage media of claim 20, whereinthe instructions, when executed by the processor, further cause thecomputing device to: generate a binary bone mask of the bone ofinterest; and generate the filled bone mask for the bone of interestusing the binary bone mask.
 22. The non-transitory computer readablestorage media of claim 20, wherein the instructions, when executed bythe processor, cause the computing device to generate the filled bonemask for the bone of interest at least by performing morphologicalprocessing of the 3-D object representing the bone of interest, saidmorphological processing comprising: generating a binary bone mask ofthe bone of interest; performing 3-D binary dilation of the binary bonemask of the bone of interest to form a dilated bone mask; andidentifying and filling borders, internal voxels, and/or morphologicalholes of the dilated bone mask, and then processing the result togenerate the filled bone mask for the bone of interest.
 23. Thenon-transitory computer readable storage media of claim 22, wherein theinstructions, when executed by the processor, cause the computing deviceto fill the borders of the bone of interest at least by: representingimage data from the binary bone mask of the bone of interest digitallyas one or more data-cubes; identifying a vertex of a data-cube, thevertex having all edges connected to the vertex associated with truevoxels; forming a 2-D image from three faces connected to the identifiedvertex of the data-cube; filling morphological holes in the formed 2-Dimage to produce a filled surface; and mapping the filled surface backto the three faces connected to the identified vertex of the data-cube.24. The non-transitory computer readable storage media of claim 20,wherein the instructions, when executed by the processor, cause thecomputing device to determine the 3-D central axis of the bone ofinterest at least by generating a thinned skeleton of the bone ofinterest.